How can I make a shape follow a profile without it following the profile normals?
In this example I use two objects "Pillar" and "Bevel" ...


select "Pillar" curve and search for Set Origin to Geometry
search Convert to Curve (both objects should be a curve)
Search Spline type >  Bezier and set handle types (V) > Automatic
under Properties Editor > Object Data > Bevel assign a curve "Bevel"
with curve "Bevel" selected go to edit mode (TAB) and rotate vertices in X -90° (so curve goes in Y axis) and move all control points to bring bottom vertex to origin position


Note: 


always good to Apply Transformations (Ctrl+A) like Scale in here
switch curves to 2D (Properties Editor > Curve Data)
I had to scale up the Pillar shape (in edit mode) up to 3 to get result where Bevel curve doesn't generates weird in thinner curvature








Edit: just from what I see on your reference image, you should probably start with five circles object, because when you bevel on final floor shape you get wrong intersections of small circles with big one. Step by step is the same. Except for Bevel Curve move control points a bit far from origin. Here is the result.